Transport and thermoelectric properties of bernal stacked bilayer graphene due to lattice vibrations and magnetic field

The impacts of electron-Einstein phonon interaction have been taken into consideration when analyzing the transport parameters of bernal layered bilayer graphene. In particular, we examine the Seebeck coefficient of the structure and the temperature dependence of thermal and electrical conductivities. Additionally, the energy dependence of state density due to the influence of bias voltage and electron-phonon coupling strength has been examined. The system's transport and thermoelectric characteristics have been examined in relation to the strength of the electron-phonon coupling and the external magnetic field. Green's function approach has been used to determine the system's electrical characteristics within the framework of the Holstein model Hamiltonian. To determine the interacting electronic Green's function, the model Hamiltonian's one loop electronic self-energy has been determined. Using interacting Green's function, it is easy to determine the electrical and thermal conductivities of bilayer graphene in the presence of electron-phonon interaction. Our findings demonstrate that the temperature dependence of bilayer graphene's thermal conductivity shows a drop in peak height as electron-phonon coupling increases. Additionally, when the intensity of the electron-phonon coupling increases, the temperature position of the peak in the temperature dependence of thermal conductivity shifts to lower values. Additionally, we have examined how the Seebeck coefficient and electrical conductivity change with temperature in response to changes in bias voltage and magnetic field intensities.